Question

Determine as raízes (zeros) reais e as coordenadas do vértice das funções f (x) = -4²x + 20x - 25

Answer 1

f(x) = - 4x^2 + 20x - 25

0 = - 4x^2 + 20x - 25

- 4x^2 + 20x - 25

a = - 4 b= 20. c = - 25

D = b^2 - 4 a c

D = (20)^2 - 4(-4)(-25)

D = 400 + 16 (-25)

D = 400 - 400

D = 0

X = - b -, + \/D
.......________
................2a

X = - (20)- , + \/0
.......__________
................2(-4)

X = - 20 - , + 0
......._________
.................- 8

X1 = - 20 - 0
........_______
....... ......- 8

X1 = - 20
........____..(÷4)
.........- 8

X1 = 5
........__
.........2

X2 = - 20 + 0
........._______
................8

X2 = - 20
...........____..(÷4)
.............- 8

X2 = 5
........___
..........2

S { 5/2 }